Abstract. We further investigate the voltage construction for triangulations by complete tripartite graphs, see paper [35] from this list. Since such triangulations are face 2-colourable, each colour class corresponds to a Latin square. We already know that both these Latin squares are isomorphic to the cyclic Latin square C defined by C(i,j)=i+j, the addition being modulo the order of C. In the paper we identify all Latin squares B which appear in these biembeddings, when the other square is exactly C. Using this result we improve the lower bound on the number of nonisomorphic triangulations obtained by the voltage construction, provided that the order is a prime number.